1. 5.3 Rate of Change and Slope 5.4 The Slope Formula
Algebra 5.3
5.3 Rate of Change and Slope
5.4 The Slope Formula

2. 5.3 Learning Targets Language Goal
Students will be able to verbally relate a constant rate of change to the slope of a line
Math Goal
Students will be able to find rates of change and slopes.
Essential Questions
Why are graphs a valuable source of information?

3. 5.3 Warm-up

4. 5.2 Homework Check

5. 5.2 Homework Check

6. 5.2 Homework Check

7. 5.3 Vocabulary Rate of Change: Rise: Run: Slope:
A ratio that compares the amount of change in a dependent variable to the amount of change in a independent variable
The difference in the x-values of two points on a line.
The difference in the y-values of two points on a line.
The ratio of rise to run for any two points on a line.

8. Rate of Change and Slope

9. Rate of Change Practice
The table shows the temperatures (in °F) at one location at different times.
1. Which is the dependent variable?
2. Which is the independent variable?
3. Calculate the rate of change for each time interval.
8 am to 11 am: ______ 11 am to 1 am: ______
1 pm to 5 pm: _______

10. Hint!!
The independent variable is usually a form of time!!!

11. Example 1: Word Problem
The table shows a truck driver’s distance from home during one day’s deliveries. Find the rate of change for each interval.
Hour 0 to Hour 1: ____ Hour 1 to Hour 4: ____
Hour 4 to Hour 5: ____ Hour 5 to Hour 8: ____
Hour 8 to Hour 10: ____
The rate of change represents the average speed. During which time interval was the driver’s average speed the least?

12. Example 2: Finding Rates of Change from a Graph
The table shows the amount of water in a pitcher at different times. Graph the data and show the rates of change.
Between which two hours is the rate of change the greatest?

13. Example 3 and 4: Finding Slope From a Graph
𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

14. Example 3 and 4: Finding Slope From a Graph
𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

15. Example 3 and 4: Finding Slope From a Graph
𝑆𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

16. Classifying Slopes

17. Example 5: Describing Slope
As the absolute value of the slope increases, the lines becomes steeper.
A. m = 0 B. m = 1 50
C. m = D. m = 2 0

18. Extra Practice Finding Slope WS
Work with a partner or individually. We will discuss as a class.
Make sure that you find a point that lies on an intersection between an x and y integer.

19. Calculate Slope Given Graph

20. Calculate Slope Given Graph

21. Calculate Slope Given Graph

22. Calculate Slope Given Graph

23. Calculate Slope Given Graph

24. Calculate Slope Given Graph

25. 5.3 Lesson Quiz